If x-y=3 then what is the value of
Created: 2 years ago |
Updated: 8 months ago
best des
We can use the formula for the difference of cubes to simplify the expression x^3 - y^3:
x^3 - y^3 = (x - y)(x^2 + xy + y^2)
Given that x - y = 3, we can rewrite the expression as:
x^3 - y^3 = 3(x^2 + xy + y^2)
Now, we need to find the value of 3(x^2 + xy + y^2) - 9xy:
3(x^2 + xy + y^2) - 9xy = 3(x^2 + 2xy + y^2 - 3xy) = 3((x + y)^2 - 3xy)
We know that x - y = 3, so x = 3 + y.
Substituting this into the expression:
3(((3 + y) + y)^2 - 3(3 + y)y) = 3((6 + 2y + y^2) - (9 + 3y)) = 3(6 + 2y + y^2 - 9 - 3y)
Now, simplify the expression:
3(6 - 3 + 2y - 3y + y^2) = 3(3 - y + y^2)
Now, we can substitute x - y = 3:
3(3 - 3 + y^2) = 3(y^2)
So, the value of 3(x^2 + xy + y^2) - 9xy is 3y^2.
Now, let's find the value of 3y^2 when x - y = 3:
3y^2 = 3(3^2) = 3(9) = 27
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